Ukraine has accused Russia of attacking power and water plants in response to Ukrainian troops' liberation of cities to the east.
An attack on a thermal power station in Kharkiv caused widespread power cuts, while a water facility was also attacked, Ukrainian officials said.
The weekend offensive forced Russia to abandon its main bastion in the Kharkiv region.
“No military facilities, the goal is to deprive people of light and heat,” Ukrainian President Volodymyr Zelenskyy wrote on Twitter late on Sunday.
Bridget Brink, the US ambassador to Ukraine, criticised the strikes.
"Russia's apparent response to Ukraine liberating cities and villages in the east: sending missiles to attempt to destroy critical civilian infrastructure," she wrote on Twitter.
Russia denies its forces deliberately picked civilian targets.
Mr Zelenskyy has described Ukraine's offensive in the north-east as a potential breakthrough in the six-month-old war. He said more territorial gains could be made in the winter if Kyiv received more powerful weapons.
In the worst defeat for Moscow's forces since they were repelled from the outskirts of the capital Kyiv in March, thousands of Russian soldiers left behind ammunition and equipment as they fled the city of Izium, which they had used as a logistics hub.
Ukraine's chief commander, Gen Valeriy Zaluzhnyi, said armed forces had regained control of more than 1,150 square miles (2,978 square kilometres) since the start of this month.
Near the Russian border, in the village of Kozacha north of Kharkiv, Ukrainian soldiers and local officials were greeted by residents with hugs and handshakes.
“Kozacha is and will be Ukraine,” district mayor Vyacheslav Zadorenko said on a video he posted on Facebook.
“No 'Russian World' whatsoever. See for yourselves where the 'Russian World' rags are lying around. Glory to Ukraine, glory to the Ukrainian armed forces.”
Moscow's silence on the defeat provoked significant anger among some pro-war commentators and Russian nationalists on social media.
Some called on Sunday for President Vladimir Putin to make immediate changes to ensure ultimate victory in the war.
Mr Zelenskiy said late on Sunday that Russian attacks caused a total power cut in the Kharkiv and Donetsk regions, as well as partial blackouts in the Zaporizhzhia, Dnipropetrovsk and Sumy regions.
Mykhailo Podolyak, an adviser to Ukraine's president, said Kharkiv’s CHPP-5 electricity station — one of the largest in Ukraine — had been hit.
"A coward 'response' for the escape of its own army from the battlefield," he wrote on Twitter.
Kharkiv governor Oleh Synehubov said 80 per cent of electricity and water supplies had been restored in the region by Monday morning.
Defence Minister Oleksii Reznikov told the Financial Times Ukraine needed to secure retaken territory against a possible Russian counter-attack on stretched Ukrainian supply lines.
But he said the offensive had gone far better than expected, describing it as a "snowball rolling down a hill".
"It's a sign that Russia can be defeated," he said.